(Original post by worriedParnt)
I may be wrong but my point is that there are two possible spheres. We start with the origin, we fix n and l which gives our plane, and now we have two places to put the sphere, "above" or "below" the plane.

EDIT: Since is given by the question to be the centre of the sphere, there is only one sphere of radius a that we need to consider.

Perhaps some input from someone more experienced would help...

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(Original post by DFranklin)
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(Original post by mikelbird)
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Starts at post 995

Last edited by Farhan.Hanif93; 14-03-2012 at 17:49.
Reason: Clarification

I think the key problem here is the question is ambiguous. Knowing the plane is "perpendicular to n" and has minimum distance l to the origin is not enough to uniquely define the plane. Your solution to (ii) seems to work on the assumption that the plane equation must be of form but is also possible.

But once you allow the ambiguity it's not actually clear what the question means. Are you looking for a conditions on the sphere such that *a* plane satisfying the requirements exists, or are you searching for requirements on the definition of the plane such that it will be tangential to the sphere?

I suspect your interpretation is the one the examiner was after, but it's not a good question.

(Original post by carlos the third)
How does the marking work in STEP? If you get about half of a question right will you get about half marks? Or are there a lot of marks just for getting the answer right?

My teacher thinks it's a "squarey" relationship - i.e. few to no marks for a fragment, then a big increase as you get closer and closer to a perfect solution.

I don't think it is - IIRC some of the reports say things like "part i) was 5 easy marks", implying there is a mark scheme they use that splits up the 20 available into parts.

I could be wrong - just reporting on what I remember! But if there's two halves of a question, each requiring the same effort, it makes sense that they should be worth 10 each.

(Original post by carlos the third)
How does the marking work in STEP? If you get about half of a question right will you get about half marks? Or are there a lot of marks just for getting the answer right?

Most of the "official statements" imply full questions score more than twice what half questions do.

My own experience of marking at Cambridge (for the Maths degree), and nearly all the evidence gleaned from how people from TSR have done in STEP, indicates that in practice, as you suggest, answering half a question will get you approximately half marks.

[I think part of the justification for the official statements is the danger hat weaker candidates will do lots of 'part-questions' that actually are a long way from even being half-solutions and so get very few marks. I think Cambridge would also "prefer" people to do 4 full questions to 2 full and 4 half-questions, and so encourage full solutions. But the actual marks given don't seem to reflect this].

(Original post by DFranklin)
[I think part of the justification for the official statements is the danger hat weaker candidates will do lots of 'part-questions' that actually are a long way from even being half-solutions and so get very few marks. I think Cambridge would also "prefer" people to do 4 full questions to 2 full and 4 half-questions, and so encourage full solutions. But the actual marks given don't seem to reflect this].

Marking is tricky because what the examiner (knowing not only the proposed solution but presumably other ways of tackling the problem) might not foresee where most people will find something difficult. Sometimes a 'simple' manipulation will defeat the majority of candidates under exam conditions. Maybe its easier to keep the marking scheme relatively level so that each part of a question gets roughly equal marks?

(Original post by shamika)
Marking is tricky because what the examiner (knowing not only the proposed solution but presumably other ways of tackling the problem) might not foresee where most people will find something difficult. Sometimes a 'simple' manipulation will defeat the majority of candidates under exam conditions.

Yeah, it's pretty clear in the TSR STEP Post Mortems that this sometimes happens. The examiners thought "everyone" would spot a 1-2 line method of doing some minor part of the question, and virtually no-one actually does.

It still doesn't really explain to me why they emphasize full questions, however.

(Original post by DFranklin)
Yeah, it's pretty clear in the TSR STEP Post Mortems that this sometimes happens. The examiners thought "everyone" would spot a 1-2 line method of doing some minor part of the question, and virtually no-one actually does.

It still doesn't really explain to me why they emphasize full questions, however.

Presumably because either

- the examiners attempt to operate an alpha/beta type system (even if it quite often fails)
- when Cambridge/Warwick/Imperial looks at scripts in the summer pool, it prefers someone with 2 full solutions (say) than 4 half-fragments?

- the examiners attempt to operate an alpha/beta type system (even if it quite often fails)

There's no evidence this is true, however. (Siklos has explicitly said there are no bonus marks for full questions, for example).

- when Cambridge/Warwick/Imperial looks at scripts in the summer pool, it prefers someone with 2 full solutions (say) than 4 half-fragments?

Somewhat of a valid point, but if you get a 1 using fragments you won't have to worry about the summer pool.

That's not particularly facetious: if you look at the 1 boundaries, for borderline cases it is actually fairly likely that it's how you do on the fragments that will end up deciding whether you get that 1.

(Original post by DFranklin)
There's no evidence this is true, however. (Siklos has explicitly said there are no bonus marks for full questions, for example).

I guess I'm out of ideas then! Because if you've established that the marks don't ramp up for later parts of the questions, and they are no bonus marks, there really isn't a penalty for fragmented answers...

(Original post by shamika)
I guess I'm out of ideas then! Because if you've established that the marks don't ramp up for later parts of the questions, and they are no bonus marks, there really isn't a penalty for fragmented answers...

I can think of 2-3 reasons why you might not want to fragment your way to victory:

You don't know how much any given fragment is worth - could be 15, could be 5. Completing answers gives you confidence.

It's often faster to continue a question than spending time to take in and attempt a whole new question. (assuming you wouldn't start all 6 anyway)

If you would start all 6 anyway, if you start one that it turns out you really can't do, you've spent that thinking time on nothing. Much better to spend the time on a few questions you definitely can do.

I'm trying to do complete solutions, but for II and III they still take me way too long. I think I'm speeding up, but after my timed STEP III past paper I know I need to work harder!

(Original post by carlos the third)
How does the marking work in STEP? If you get about half of a question right will you get about half marks? Or are there a lot of marks just for getting the answer right?

STEP mark schemes are not published. But the examiner's guide gives some hints. Try Dr Julian Gilbey's recent STEP I reports on the Cambridge Assessment website.

I believe the following statements to be true:

(1) the mark scheme resembles A level in that there are A(ccuracy) and M(ethod) marks.

(2) there are many more M marks than A marks

(3) whilst there may once have been 'alphas' for basically complete solutions as in the Tripos, there are no longer.

(4) if a simple 'show' is omitted at the start of a question you are not precluded from scoring the majority of the marks for later parts.

(5) a simple first part may score 5/20 leaving 15/20 for the harder second part.

(Original post by Farhan.Hanif93)
EDIT: Since is given by the question to be the centre of the sphere, there is only one sphere of radius a that we need to consider.

Perhaps some input from someone more experienced would help...

Quotes

Starts at post 995

Let's look at an example.

d=(5,0,0)
a=1
n=(1,0,0)

so we have n.d=5. There are two possible values of l, 6 and 4 corrsponding to planes tangential at the north pole (6,0,0) and the south pole (4,0,0). I don't see how n.d = l-a picks up the south pole solution. i believe the mistake in your proof is when you assert that the radius of the sphere is parallel to n. It can be anti-parallel.

Sorry, don't know where else to post this. If I were to apply to a university that doesn't require STEP (ie. Bristol, I'm a Scottish applicant), but I had sat the test anyway, would the admissions people know, or care?

Physical NatSci reapplicant 2013, tempted to sit STEP at the end of this year, probably just STEP I. Help or hindrance? I mean I'm quite sure I'll achieve 3A*A or 4A*, and I have spare time each evening that I tend to use up reading (fiction) books.

I like maths, and have succeeded in getting partial solutions (as in, almost full) to the few questions I've tried. Do I take the plunge? ^_^

(Original post by Oromis263)
I like maths, and have succeeded in getting partial solutions (as in, almost full) to the few questions I've tried. Do I take the plunge? ^_^

I have to be honest, it worries me when someone keeps getting "partial / almost full" solutions.

I'd say it's actually quite unusual to "almost" do a STEP question. The last part of the question is usually worth a fair number of marks and it tends to be a bit "all or nothing" in terms of progress.

My gut feeling is someone who thinks they have many such solutions is probably overestimating how much of the question they've done.

[If you meant you can finish the questions, but often have a small mistake somewhere, that's different].

(Original post by DFranklin)
I have to be honest, it worries me when someone keeps getting "partial / almost full" solutions.

I'd say it's actually quite unusual to "almost" do a STEP question. The last part of the question is usually worth a fair number of marks and it tends to be a bit "all or nothing" in terms of progress.

My gut feeling is someone who thinks they have many such solutions is probably overestimating how much of the question they've done.

[If you meant you can finish the questions, but often have a small mistake somewhere, that's different].

This, but I understand where you're coming from. Oh, and your opinion on my question? I mean, it's quite something to undertake..